with your host… alan quebec. group theory orbits and counting coding theorypotpourri $100 $200...

With your host…Alan Quebec

Group theoryOrbits and counting

Coding theory

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The four group axioms

Back

ClosureAssociativity

IdentityInverses

A group with 11 elements is this kind of group

Back

Cyclic

The easiest way to tell if a subset of G is a subgroup

Back

Check that if x, y are elements of H, then so is

xy-1

Why S5 cannot have a subgroup of order 7

Back

Lagrange’s Theorem

There are this many elements of order 13 in

C13

Back

12 (1 has order 1)

The difference between Gx and Gx

(Not just the names of the terms, but their meanings)

Back

Gx is the orbit containing x; Gx is the stabilizer of x

The size of an orbit if G = S4

Back

4

The number of ways to color the edges of a pentagon red, green,

and blue

Back

The number of ways to place colored pie slices into a Trivial Pursuit game piece like

the one below, if only the orange and yellow pieces can be used

Back

The number of ways to color the edges of a pentagon red, green, and blue where 2 edges are green and 2

edges are blue

Back

Back

Coefficient of rb2g2 is

The number of errors that this code can correct for:00000, 01100, 00111, 11001

Back

0 (minimum distance is 2)

The length of a codeword in the linear code given by the

associated matrix

Back

7

The maximum number of codewords in a code of length 7 that can correct for one

error

Back

16, since

The number of codewords in the linear code given by the

associated matrix

Back

24 = 16

This is the smallest linear code that contains the codewords

001, 110

Back

000, 100, 011, 111(code must be a group)

These three sets are all rings

Back

A ring that is not a field has this distinguishing

characteristic

Back

Not all nonzero elements have multiplicative inverses

This is an example of an invertible power series where all coefficients are nonzero and the coefficient of

is 10

Back

Any matching power series that has a invertible constant term

The parity (even or odd) of the permutation (12345)

Back

Even; decomposition into transpositions is (12)(23)(34)(45)

The order of the permutation(12)(345)

Back

lcm(2, 3) = 6